Question

A body of mass 3kg under a force , which causes a displacement in it is given by s=t^3/3 in m. Find the work done by the force in first 2 seconds

Answer 1

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$s=\large\frac{1}{3}$$t^2=>\large\frac{ds}{dt}=\frac{2}{3}$$t$

acceleration $=a=\large\frac{d^2s}{dt^2}$

$\qquad=\large\frac{2}{3}$$m/s^2$

Force $=m \times a$

$ \qquad=3 \times \large\frac{2}{3}$$=2N$

$ds=\large\frac{2}{3}$$tdt$

Work done $= \int F ds$

$W=F \int \limits_0^t \large\frac{2}{3} $$t dt$

$\quad=2 \times \large\frac{2}{3} $$ \times \large \frac{t^2}{2} \bigg|_0^2$

$\quad=\large\frac{4}{3} \times \frac{4}{2}$

$\quad=\large\frac{8}{3}$$\;J$

Hence a is the correct answer.